PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Integrated Pearson family and orthogonality of the Rodrigues polynomials: A review including new results and an alternative classification of the Pearson system

Volume 42 / 2015

G. Afendras, N. Papadatos Applicationes Mathematicae 42 (2015), 231-267 MSC: Primary 62E15, 60E05; Secondary 62-00. DOI: 10.4064/am42-2-9

Abstract

An alternative classification of the Pearson family of probability densities is related to the orthogonality of the corresponding Rodrigues polynomials. This leads to a subset of the ordinary Pearson system, the so-called Integrated Pearson Family. Basic properties of this family are discussed and reviewed, and some new results are presented. A detailed comparison between the Integrated Pearson Family and the ordinary Pearson system is presented, including an algorithm that enables one to decide whether a given Pearson density belongs, or not, to the integrated system. Recurrences between the derivatives of the corresponding orthonormal polynomials are also given.

Authors

  • G. AfendrasDepartment of Biostatistics
    University at Buffalo
    Buffalo, NY 14214, U.S.A.
    e-mail
  • N. PapadatosDepartment of Mathematics
    Section of Statistics and O.R.
    University of Athens
    Panepistemiopolis
    157 84 Athens, Greece
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image